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The structure of elements in finite full transformation semigroups

Published online by Cambridge University Press:  17 April 2009

Gonca Ayik
Affiliation:
Department of Mathematics, Çukurova University, Adana, Turkey, e-mail: hayik@mail.cukurova.edu.tr
Hayrullah Ayik
Affiliation:
Department of Mathematics, Çukurova University, Adana, Turkey, e-mail: hayik@mail.cukurova.edu.tr
Yusuf Ünlü
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, United Kingdom, e-mail: jmh@st-and.ac.uk
John M. Howie
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, United Kingdom, e-mail: jmh@st-and.ac.uk
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The index and period of an element a of a finite semigroup are the smallest values of m ≥ 1 and r ≥ 1 such that am+r = am. An element with index m and period 1 is called an m-potent element. For an element α of a finite full transformation semigroup with index m and period r, a unique factorisation α = σβ such that Shift(σ) ∩ Shift(β) = ∅ is obtained, where σ is a permutation of order r and β is an m-potent. Some applications of this factorisation are given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

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